What kind of road and weather conditions can a self-driving car deal with?
No, smart cars do not know what to do when surrounded with ducks or flood waters, and it's possible they never will.  

As with all machine learning, a computer knows only what it's taught.  If an event arises that's unusual, the AI will have less relevant training on how to respond, so its reaction behavior necessarily will be inferior to its routine "standard operating procedure", for which is has been heavily trained.  (Of course this is true of humans too.)

Due to liability concerns, when encountering an outlier condition, smart cars will almost certainly be designed by their makers to immediately pull off the road and wait to be explicitly told what to do -- by the human in the car or by communicating with a central command office that exists to disambiguate such confusion and resolve cognitive impasses.  When confused, just like a child, a smart car will be designed to seek external assistance -- and is likely to do so indefinitely, I suspect.

That's why, despite Google's recent cars that lack steering wheels, smart cars most certtainly will retain some means of manual control -- be it a wheel and pedals, or at least verbal commands.  Given the many forms of weirdness that are possible on the road, it's possible smart cars will never be fully autonomous.

As for bad weather conditions, how well do smart cars currently perform?  Nobody outside of a car manufacturer can say for certain.  Lidar and radar are superior to the human eye in seeing through fog and snow.  But (competent) humans are likely to remain better than a smart car at dynamically learning the limit of adhesion and compensating (since this is a learned skill few smart cars will already know or can learn quickly -- given this car, these tires, this road surface, this angle of road, etc).

Initially smart cars will turn to the human when the going gets rough, ceding control back to them.  Once smart cars have driven a few million miles in snow, slush, high wind, floods, and ice, and encountered many ducks, angry mooses, and irate pedestrians, they will have been taught to do more for themselves.  Until then, and perhaps for decades yet, I suspect they will turn to mommy and ask for help.